UPSC Prelims 2009 · General Studies

Question 100: Basic Numeracy

While adding the first few continuous natural numbers, a candidate missed one of the numbers and wrote the answer as 177. What was the number missed?

a11

b12

c13

d14

AnswerThe answer is (c).

The sum of 1 to n is n(n+1)/2. The wrong total of 177 is below the true sum, so n(n+1)/2 must be just above 177. For n = 18 the sum is 171, too small; for n = 19 it is 190. The missed number is 190 - 177 = 13. For n = 20 the sum is 210 and the gap 33 is larger than 20, so impossible.

Why each option is right or wrong

(a) Missing 11 would give a total of 179, not 177.
(b) Missing 12 would give a total of 178.
(c) Right: 190 - 13 = 177.
(d) Missing 14 would give a total of 176.

Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2009, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.